Identifying the number of clusters: finally a solution

It optimizes the number of the cluster when the clustering method is maximizing the variance among the clusters. If you are using for example K-means as clustering algorithm, your method will fail for every number of cluster you try to use! As you can see doesn't exist the right number of clusters, for this problem using the "naive" kmeans. BTW I've seen for kmeans and density based clustering algo, methods based on EM (expectation and maximizazion) and Bayesian information criterion (BIC) that are a little bit more robust than this method. Could you share the table of the points...just to play a little bit with them:)